-x-6=5/9x+8

Solution for -x-6=5/9x+8 equation:

-x-6=5/9x+8

We move all terms to the left:

-x-6-(5/9x+8)=0


Domain of the equation: 9x+8)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(5/9x+8)-6=0

We get rid of parentheses

-1x-5/9x-8-6=0

We multiply all the terms by the denominator


-1x*9x-8*9x-6*9x-5=0

Wy multiply elements

-9x^2-72x-54x-5=0

We add all the numbers together, and all the variables

-9x^2-126x-5=0

a = -9; b = -126; c = -5;
Δ = b2-4ac
Δ = -1262-4·(-9)·(-5)
Δ = 15696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15696}=\sqrt{144*109}=\sqrt{144}*\sqrt{109}=12\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-12\sqrt{109}}{2*-9}=\frac{126-12\sqrt{109}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+12\sqrt{109}}{2*-9}=\frac{126+12\sqrt{109}}{-18}
$